Draw Path On Android MapView

Google MyTracks
http://code.google.com/p/mytracks/source/browse/MyTracks/src/com/google/android/apps/mytracks/MapOverlay.java

Other Sample Code
http://stackoverflow.com/questions/4408671/android-draw-route-on-a-mapview-with-twoo-poi-s

Background Log GPS
http://code.google.com/p/gpslogger/source/browse/trunk/GPSLogger/src/com/prom2m/android/gpslogger/service/GPSLoggerService.java